Growth and uniqueness of rank

Eli Aljadeff; Shmuel Rosset

doi:10.1007/BF02787226

Growth and uniqueness of rank

Eli Aljadeff^*, Shmuel Rosset

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We prove that algebras of sub-exponential growth and, more generally, rings with a sub-exponential "growth structure" have the unique rank property. In the opposite direction the proof shows that if the rank is not unique one gets lower bounds on the exponent of growth. Fixing the growth exponent it shows that an isomorphism between free modules of greatly differing ranks can only be implemented by matrices with entries of logarithmically proportional high degrees.

Original language	English
Pages (from-to)	251-256
Number of pages	6
Journal	Israel Journal of Mathematics
Volume	64
Issue number	2
DOIs	https://doi.org/10.1007/BF02787226
State	Published - Jun 1988
Externally published	Yes

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10.1007/BF02787226

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title = "Growth and uniqueness of rank",

abstract = "We prove that algebras of sub-exponential growth and, more generally, rings with a sub-exponential {"}growth structure{"} have the unique rank property. In the opposite direction the proof shows that if the rank is not unique one gets lower bounds on the exponent of growth. Fixing the growth exponent it shows that an isomorphism between free modules of greatly differing ranks can only be implemented by matrices with entries of logarithmically proportional high degrees.",

author = "Eli Aljadeff and Shmuel Rosset",

year = "1988",

month = jun,

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AU - Aljadeff, Eli

AU - Rosset, Shmuel

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N2 - We prove that algebras of sub-exponential growth and, more generally, rings with a sub-exponential "growth structure" have the unique rank property. In the opposite direction the proof shows that if the rank is not unique one gets lower bounds on the exponent of growth. Fixing the growth exponent it shows that an isomorphism between free modules of greatly differing ranks can only be implemented by matrices with entries of logarithmically proportional high degrees.

AB - We prove that algebras of sub-exponential growth and, more generally, rings with a sub-exponential "growth structure" have the unique rank property. In the opposite direction the proof shows that if the rank is not unique one gets lower bounds on the exponent of growth. Fixing the growth exponent it shows that an isomorphism between free modules of greatly differing ranks can only be implemented by matrices with entries of logarithmically proportional high degrees.

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U2 - 10.1007/BF02787226

DO - 10.1007/BF02787226

M3 - 文章

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SN - 0021-2172

VL - 64

SP - 251

EP - 256

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 2

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Growth and uniqueness of rank

Abstract

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